As of the time of this question, there are talks that Manchester City may be banned from the UEFA Champions League 2019-20 competition.
If a top-four English Premier League team is banned, who takes the vacant slot?
Teams of the English Premier League can earn a maximum of five places between them in the UEFA Champions League, and a maximum of seven places in all European continental competition.
Those places are allocated as follows:
Winner of UCL 18-19, if any
Winner of UEL 18-19, if any
EPL 18-19 #1
EPL 18-19 #2
EPL 18-19 #3
EPL 18-19 #4 (gets dropped to UEL 19-20 if all five previous places are allocated already)
Thus for UCL 19-20, the allocation is currently held by
Liverpool or Tottenham Hotspur
Arsenal or Chelsea
& 5. Liverpool or Chelsea or Tottenham Hotspur (if not already qualified)
Arsenal (if not already qualified) (gets dropped to UEL 19-20 if placed here)
If Manchester City is removed, the remaining four teams between them are allocated four places, with the UCL place doubling up, and therefore England's allocation is done.
The exception to this is with Arsenal placed fifth, as they would not otherwise qualify, leaving an unallocated place, but it would be nonsensical to give it to a team ranked lower (e.g. Manchester United in sixth) instead, therefore Arsenal would likely go in place either way.